document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358880>Question 358880</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Throwing a wrench. An angry construction worker throws<BR>\n" );
document.write( "his wrench downward from a height of 128 feet with an<BR>\n" );
document.write( "initial velocity of 32 feet per second. The height of the<BR>\n" );
document.write( "wrench above the ground after t seconds is given<BR>\n" );
document.write( "by S (t) = -16t^2 – 32t + 128<BR>\n" );
document.write( "a) What is the height of the wrench after 1 second?<BR>\n" );
document.write( "b) How long does it take for the wrench to reach the<BR>\n" );
document.write( "ground?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256199 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> worker throws his wrench downward from a height of 128 feet with an<BR>\n" );
document.write( "initial velocity of 32 feet per second.<BR>\n" );
document.write( " The height of the wrench above the ground after t seconds is given by<BR>\n" );
document.write( " S(t) = -16t^2 – 32t + 128<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) What is the height of the wrench after 1 second?<BR>\n" );
document.write( "S(t) = the height, t=1; therefore:<BR>\n" );
document.write( "S(t) = -16(1^2 - 32(1) + 128<BR>\n" );
document.write( "S(t) = -16 - 32 + 128<BR>\n" );
document.write( "S(t) = 80 ft after one second<BR>\n" );
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document.write( "b) How long does it take for the wrench to reach the ground?<BR>\n" );
document.write( "Replace height [S(t)] with ground level, which is 0<BR>\n" );
document.write( "-16t^2 - 32t + 128 = 0<BR>\n" );
document.write( "Simplify and change the signs, divide equation by -16<BR>\n" );
document.write( "t^2 + 2t - 8 = 0<BR>\n" );
document.write( "Factor <BR>\n" );
document.write( "(t+4)(t-2) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "t = 2 seconds for the wrench to reach the ground<BR>\n" );
document.write( ":<BR>\n" );
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document.write( "We can prove this: <BR>\n" );
document.write( "S(t) = -16(2^2) - 32(2) + 128<BR>\n" );
document.write( "S(t) = -16(4) - 64 + 128<BR>\n" );
document.write( "S(t) = -64 - 64 + 128<BR>\n" );
document.write( "S(t) = 0<BR>\n" );
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document.write( "Did this make sense to you now? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );